WO2021216473A1

WO2021216473A1 - Assembly system

Info

Publication number: WO2021216473A1
Application number: PCT/US2021/028024
Authority: WO
Inventors: Rachel HOFFMAN; Haruhiko Harry Asada
Original assignee: Massachusetts Institute Of Technology
Priority date: 2020-04-20
Filing date: 2021-04-19
Publication date: 2021-10-28
Also published as: WO2021216473A8; JP2023522105A; CN115776969A

Abstract

An apparatus and method for placing a first object into a chamfered cavity of a second object is disclosed. In some embodiments, the first object is suspended from a plurality of flexible tethers such that the flexible tethers retain the first object in an orientation suitable for insertion into the second object.

Description

ASSEMBLY SYSTEM CROSS-REFERENCE TO RELATED APPLICATIONS This application claims the benefit under 35 U.S.C. § 119(e) of U.S. Provisional Patent Application Serial No.63/012,363, filed April 20, 2020 and entitled “Apparatus and Method of Precision Assembly of Objects Suspended with Multiple Cables,” which is incorporated herein by reference in its entirety. FIELD Disclosed embodiments relate to assembly systems and methods, for example, systems and methods that place objects using multiple tethers. BACKGROUND When assembling objects in heavy industries (e.g., aerospace, shipbuilding, mining, etc.), heavy workpieces and subassemblies may need to be accurately positioned against other objects and/or structures. Typically, fine positioning and/or mating crane-hung objects may require special training and/or experience, making typical object assembly largely dependent on skilled labor. In general, assembly may be performed by workers that stand near a crane-hung object and adjust the position and orientation of one or more objects by directly pushing and/or pulling the one or more objects, while adjusting the height of the crane. BRIEF SUMMARY According to one aspect, an assembly apparatus includes a support structure; a plurality of tethers suspended from the support structure, the plurality of tethers configured to suspend a first object from the support structure; and one or more actuators operatively coupled to at least one selected from the group of the support structure and the plurality of tethers, the one or more actuators configured to lower a portion of the first object under an influence of gravity towards a cavity formed in a second object with a chamfer formed along at least a portion of the cavity, and wherein the one or more actuators and the plurality of tethers are configured to control the lowering of the portion of the object such that the portion of the first object contacts and slides along the chamfer as the portion of the first object is inserted into the cavity. According to another aspect, a method of placing an object in a cavity includes suspending a first object from a plurality of tethers of an assembly apparatus; lowering a portion of the first object under an influence of gravity towards a cavity formed in a second object with a chamfer formed along at least a portion of the cavity such that at least a portion of the first object makes contact with the chamfer; sliding the portion of the first object along the chamfer; and placing the first object in the cavity of the second object. It should be appreciated that the foregoing concepts, and additional concepts discussed below, may be arranged in any suitable combination, as the present disclosure is not limited in this respect. Further, other advantages and novel features of the present disclosure will become apparent from the following detailed description of various non-limiting embodiments when considered in conjunction with the accompanying figures. BRIEF DESCRIPTION OF DRAWINGS Non-limiting embodiments of the present disclosure will be described by way of example with reference to the accompanying figures, which are schematic and are not intended to be drawn to scale. In the figures, each identical or nearly identical component illustrated is typically represented by a single numeral. For purposes of clarity, not every component is labeled in every figure, nor is every component of each embodiment of the disclosure shown where illustration is not necessary to allow those of ordinary skill in the art to understand the disclosure. In the figures: Fig.1 is a front view of a passive assembly apparatus according to one illustrative embodiment; Fig.2A is a front view of a hung object making contact with a chamfer of a cavity of a stationary object, according to one illustrative embodiment; Fig.2B is a front view of a hung object making contact with one point of an inner wall of a cavity of a stationary object, according to one illustrative embodiment; Fig.2C is a front view of a hung object making contact with two points of an inner wall of a cavity of a stationary object, according to one illustrative embodiment; Fig.3A is a front view of an object hung from a plurality of flexible tethers according to one illustrative embodiment; Fig.3B is a front view of an object hung from a plurality of flexible tethers according to another illustrative embodiment; Fig.4 is a front view of an active assembly apparatus according to one illustrative embodiment; Fig.5 is a flowchart showing a method of passively placing a first object in a cavity of a second object; Fig.6 is a flowchart showing a method of actively placing a first object in a cavity of a second object; Fig.7 is a front view of an exemplary assembly apparatus according to one illustrative embodiment; Fig.8 is a front view of an assembly apparatus according to one illustrative embodiment; Fig.9 is a graph showing a relationship between a coefficient of friction of a chamfer of a stationary object and initial angles of flexible tethers of an assembly apparatus according to one experiment; Fig.10 is a graph showing an experimentally measured relationship between initial angles of flexible tethers of an assembly apparatus and a depth at which two-point contact between portions of a hung object and an inner wall of a cavity of a stationary object may be achieved; Fig.11 is a graph showing an experimentally measured relationship between a depth of travel and a distance from a center of a hung object and a center of a cavity; Fig.12 is a graph showing a relationship between a coefficient of friction of a chamfer of a stationary object and an initial angle of flexible tethers according to one embodiment; Fig.13 is a graph showing a relationship between a coefficient of friction of a chamfer of a stationary object according to another embodiment; Fig.14 is a graph showing a relationship between a coefficient of friction of a chamfer of a stationary object according to yet another embodiment; Fig.15A is a front view of an exemplary assembly apparatus according to one illustrative embodiment; Fig.15B is a front view of the portion of the assembly apparatus of Fig.15A contacting a surface and the resulting forces based on a location of the instantaneous center of rotation according to one embodiment; Fig.15C is a front view of the portion of the assembly apparatus of Fig.15A contacting a surface and the resulting forces based on a location of the instantaneous center of rotation according to one embodiment; Fig.15D is a front view of the portion of the assembly apparatus of Fig.15A contacting a surface and the resulting forces based on a location of the instantaneous center of rotation according to one embodiment; and Fig.15E is a front view of the portion of the assembly apparatus of Fig.15A contacting a surface and the resulting forces based on a location of the instantaneous center of rotation according to one embodiment. DETAILED DESCRIPTION Assembling objects is an important task in heavy industries (e.g., aerospace, shipbuilding, mining, etc.). To assemble such objects, accurate positioning and/or placement of heavy workpieces and/or subassemblies (e.g., heavier than 25 Kg) against other workpieces and/or subassemblies may be desired, which in many cases may prove to be a challenging task. Typically, fine positioning or mating of crane-hung objects may be particularly difficult. For example, a worker may assemble heavy objects by standing near a crane-hung object and adjusting the position and/or orientation of the object by directly pushing and/or pulling the object, while adjusting the height of the crane. The worker may push a particular part of the object steadily such that the orientation of the object may be aligned with a reference line without overshoot. In some instances, it may be particularly challenging to mate the hung object with a second object, such as a stationary structure. The hung object may be lowered with a specified position and orientation such that the object may be seated in the structure stably and with a high level of precision. This may involve a worker coordinating the crane to lower the hung object while manipulating location and/or orientation of the hung object within a horizontal plane. Such precision assembly is employed in a wide variety of application, including turbine generators, ships, and construction machines, as well as their components including large gearboxes and motors. To perform these operations quickly, a worker may need to have many years of experience and/or substantial training. In view of the above, the inventors have recognized the advantages associated with constructions and systems that may help guide a hung object into a desired position and/or orientation relative to a cavity of an object located vertically below the hung object as the objects are mated with one another. Accordingly, in some embodiments, a first hung object may be suspended from an assembly apparatus by a plurality of tethers. The first hung object may then by lowered (e.g., by the assembly apparatus) towards a secondary stationary object under an influence of gravity. In turn, the second stationary object may include a cavity for receiving the first hung object with a chamfer that extends at least partially around a perimeter of the cavity. The hung object may be roughly positioned such that a portion of the first hung object makes contact with the chamfer as the first hung object is lowered towards the cavity. Once the first hung object makes contact with the chamfer, movement of the first hung object may be controlled such that the portion of the hung object contacting the chamfer slides along the chamfer in a direction that is at least partially oriented inwards along the chamfer surface towards the cavity. The first hung object may then be placed in the cavity of the second stationary object once the object is received in the cavity. For example, in some embodiments, the first hung object may slide along the chamfer towards the cavity before making contact with an inner wall of the cavity at one point. After making contact with the inner wall of the cavity at one point, the first hung object may subsequently make contact with the inner wall of the cavity at a second point, stabilizing the first object within the cavity prior to being lowered further into the cavity. To enable the above desired functionality, in some embodiments, an assembly apparatus according to the present disclosure may include a support structure and a plurality of flexible tethers extending from the support structure. The plurality of flexible tethers may be configured to hang a first object from the flexible tethers in a desired orientation during insertion. Further in some embodiments, the plurality of tethers may be configured to maintain the tension in each tether above a predetermined tension for each tether as the first hung object is lowered towards the cavity of the second stationary object. Depending on the particular embodiment, this may be due to the tethers having a predetermined length. However, in other embodiments, the tension in each of the tethers may be actively controlled by one or more actuators to maintain the tension in each tether above the associated predetermined tension such that the first hung object is oriented approximately upright as the first hung object is lowered towards the cavity of the second stationary object and slides across the chamfered surface into the cavity. Depending on the desired application and object geometries, the systems and methods disclosed herein may be used to orient and place objects into cavities relative to either within a two-dimensional reference plane and/or within a three-dimensional environment. In view of the above, in some embodiments, it may be desirable to maintain an orientation of a first hung object relative a cavity of a second stationary object disposed vertically below the first hung object in two dimensions which are perpendicular to one another (e.g., the vertical and horizontal dimensions). In such instances, an assembly apparatus may include at least two flexible tethers from which the first object may be suspended. The flexible tethers may serve to hold the first object in a desired orientation relative to the cavity while the first object is moved by the support structure and/or the tethers. Particularly, the support structure may raise or lower the first object while the tethers maintain an orientation of the first object. Alternatively or additionally, the flexible tethers may raise and/or lower the first object by modifying the length of the tethers, for example by extending and/or retracting the tethers. In either case, the tethers may be appropriately tensioned (e.g., actively or passively, as described in greater detail herein) to maintain a desired orientation of the first object relative to the cavity both prior to and during insertion. As noted above, in some embodiments, it may be desirable to maintain an orientation of a first hung object in three dimensions relative to three perpendicular axes. In such instances, an assembly apparatus may include at least three flexible tethers in to properly position and maintain the orientation of the first object in three-dimensional space (e.g., perpendicular X, Y, and Z axes). Tensioning in the tethers as the first hung object is lowered into a cavity of the second object may be appropriately maintained and/or controlled to facilitate insertion of a portion of the first object into the cavity of the second object as elaborated on further below. In the various embodiments described herein, including the embodiments described above, assembly apparatuses including two and three tethers are described. However, it should be understood that an assembly apparatus according to the present disclosure may include any suitable number of tethers, including four tethers, five tethers, six or more tethers, and/or any other appropriate number of tethers may be used depending on the application. However, due to increasing numbers of tethers increasing the constraint of the hung object during assembly, there may be advantages to using two tethers and three tethers for positioning an object within a two- dimensional reference plane and a three-dimensional space respectively. In some instances, an assembly apparatus may be capable of carrying out an insertion process (e.g., as described above) in any suitable manner. For example, in some embodiments, the insertion process is carried out passively. In such embodiments, the assembly apparatus is configured such that the support structure is moved to move the object, while the tethers connected to the support structure maintain a desired tension under a force of gravity to control an orientation of an object as it is inserted into a cavity. For example, in such embodiments, the first object may be suspended from tethers with fixed lengths that are configured to control motion of the object relative to the cavity as the object is lowered. To lower the object the support structure may be lowered, which lowers the tethers and in turn the first object. Such functionality may be executed using a crane, a moveable gantry arrangement, or any other suitable system capable of controlling the vertical displacement of support structure and the connected object, depending on the application. Alternatively or additionally to the above, in some instances, an assembly apparatus may be capable of controlling an insertion process actively. Particularly, in some embodiments, the tensions and/or lengths associated with each of the flexible tethers may be actively controlled using one or more actuators operatively coupled to the tethers while the assembly apparatus is inserting a first object into a cavity of a second object. For example, the tethers may be connected to displaceable arms, an actuated tether spool, or other actuated systems capable of manipulating the length and/or tension of the tethers extending out from the support structure the tethers are connected to. In some embodiments, a length and/or tension of each tether of the plurality of tethers may be independently controlled which may allow the assembly apparatus to adapt to a wide array of applications. As will be appreciated by one of skill in the art, the tethers may be actively controlled during insertion in any suitable manner, depending on the application and as elaborated on below. In some instances, it may be desirable for the active control of each tether to be automated. For example, active control of the tethers may be carried out by a processor. In such an embodiment, one or more processors may be operatively coupled to the one or more actuators associated with the plurality of tethers to control operation of the one or more actuators. Specifically, the one or more processors processor may be configured to control one or more parameters of the tethers (e.g., length and/or tension). In some embodiments, this may include active feedback control. For example, one or more sensors may be configured to sense a tension and/or length of each tether. In some embodiments, this may correspond to separate sensors being associated with each tether. In either case, the signals associated with the sensed parameters may be output to the one or more processors. The one or more processors may then control the tension and/or length of the plurality of tethers based at least in part on the sensed parameters obtained from one or more sensors. An assembly apparatus may employ any suitable type of sensor for sensing the above noted parameters. For example, a tension applied to the tethers of an assembly apparatus may include one or more of a load cell, a force sensor, an extensometer, a strain gauge, and/or any other appropriate sensor configured to sense a tension or load applied to the associated tether. With regards to the extension of the one or more tethers, appropriate sensors may include, but are not limited to, actuator encoders, and/or any other appropriate type of sensor configured to sense or otherwise determine a length of the associated tether extending out from a corresponding support structure. Of course, while specific sensors are noted above, as will be appreciated by one of skill in the art, any suitable sensor or combination of sensors may be employed with the disclosed systems as the disclosure is not limited in this fashion. In some embodiments, the flexible tethers may be angled relative to a horizontal plane of a hung object (e.g., a plane perpendicular to the direction of gravity) in any suitable manner. It should be appreciated that such a range of appropriate angles may be based at least in part on the geometry of an object hung from the tethers. Particularly, the angles may be set such that the hung object may be oriented to limit the degree by which the hung object may tilt while moving towards (e.g., along a chamfer) and/or entering a cavity of a stationary object and transitioning towards a two-point contact state (e.g., as described in greater detail herein). In some instances, configuring the tethers with an appropriate angle may serve to prevent the hung object from sticking and/or binding within the cavity and/or along the chamfer. In view of the above, the angles may be set such that the flexible tethers may instantaneously rotate the hung object about a predetermined point of rotation in an effort to prevent binding and/or sticking. Without wishing to be bound by theory, the hung object may tend to rotate about an instantaneous center of ration defined by an imaginary point where lines that are parallel and coaxial with the tethers intersect with one another. To prevent binding and/or sticking, the instantaneous center of rotation may be located above or below a lower surface of a hung object (e.g., the surface oriented towards a cavity of a stationary object) by a predetermined distance. Depending on the geometry of a hung object, the angles of the tethers relative to a plane that is perpendicular to the direction of gravity may be any suitable value depending on the desired application as elaborated on below for several configurations. Specifically, there may be both upper and lower suitable ranges for the applied angles due to undesirable sticking and/or stationary behaviors occurring for certain ranges of tether angles. Particularly longer hung objects may allow for a greater range of appropriate angles, while shorter objects may have a smaller range of appropriate angles. Exemplary ranges that might be used in some applications are provided below. In some embodiments, the tethers of an assembly apparatus may exhibit appropriate tether angles (e.g., angles formed between a tether and a plane perpendicular to the direction of gravity) for a first operating range of angles to avoid sticking and/or stationary behavior of an object during insertion. These tether angles may be less than or equal to 90 degrees, 85 degrees, 80 degrees, and/or any other appropriate angle. Correspondingly, the tethers of an assembly apparatus may have a range of appropriate tether angles that is greater than or equal to 75 degrees, 80 degrees, 85 degrees, and/or any other appropriate angles. Combinations of the above-noted ranges are contemplated, including, but not limited to, angles between or equal to 75 degrees and 90 degrees. Of course, any suitable range of tether angles may be employed, depending on the application. Alternatively or additionally, in some embodiments, the tethers of an assembly apparatus may be arranged to operate within a second operating range of angles to avoid sticking and stationary behavior of an object during insertion. For example, depending on the geometry of a hung object, a range of appropriate tether angles may be less than or equal to 70 degrees, 60 degrees, 50 degrees, and/or any other appropriate angle. Correspondingly, the tethers of an assembly apparatus may have tether angles that are greater than or equal to 1 degree, 10 degrees, 20 degrees, and/or another appropriate angle. Combinations of the above-noted ranges are contemplated, including, but not limited to, tether angles between or equal to 1 degree and 70 degrees. Of course, any suitable range of tether angles may be employed, depending on the application. In some embodiments, the tether angles may be set such that the tethers do not cross when a hung object is suspended from the tethers. Accordingly, in some embodiments, teether angles between or equal to approximately 0 degrees and 120 degrees are also contemplated. In some embodiments, a range of appropriate tether angles may depend on an overall length of a hung object. For example, in some embodiments including a hung object with a relatively short overall length, tether angles of less than or equal to 50 degrees or greater than or equal to 80 degrees may be employed. Alternatively or additionally, in some embodiments including a hung object with a relatively long overall length, tether angles of less than or equal to 80 degrees may be employed. Of course, embodiments having other appropriate tether angles are also contemplated, depending on the geometry of the hung object and/or other factors as appropriate. It should be appreciated that while in some instances, the angles for each tether of a plurality of tethers are the same, embodiments where each tether takes on a different angle are also contemplated, as the disclosure is not limited in this fashion. Of course, any suitable combination of angles may be employed, depending on the application. As described herein, an instantaneous center of rotation of a hung object may be offset from a bottom surface of the hung object by a predetermined distance in a direction that is parallel to a direction of gravity to prevent binding and/or sticking. Additionally, in some embodiments, the instantaneous center of rotation of an object may be positioned such that it is above a center of mass of the hung object or below a lower most surface of the hung object relative to a direction of gravity. In some embodiments, the offset may be a percentage of a maximum dimension of the hung object parallel to a direction of gravity prior to making contact with a stationary object (e.g., an overall length of the hung object). In some embodiments, the offset distance may be greater than or equal to 50%, 60%, 70%, and/or another appropriate percentage of a length of the hung object parallel to the direction of gravity. Correspondingly, the offset distance may be less than or equal to 200%, 100%, 90%, 80%, and/or any another appropriate percentage of the maximum dimension of the hung object parallel to the direction of gravity. Combinations of the above-noted ranges are contemplated, including, but not limited to, percentages between or equal to 50% and 200%. Of course, any suitable offset distance percentage for a desired application, including percentages both smaller and larger than those noted above, may be employed, depending on the application. An assembly apparatus according to the present disclosure may include flexible tethers of any suitable type that are configured to support an object from a support structure the tethers are coupled to. For example, the flexible tethers may be cables, wires, ropes, chains, woven straps, combinations of the forgoing, and/or any other suitable elongated flexible structure capable of hanging an object from a support structure. Thus, as will be appreciated by one of skill in the art, any suitable type of flexible tether or combination of types of flexible tethers may be employed, depending on the application. An assembly apparatus according to the present disclosure may be used in any suitable application. For example, in some embodiments, the assembly apparatus may be attached to or otherwise be part of a gantry crane assembly, a crane, or other support structure for placing a first object into a cavity of a second object. Alternatively or additionally, an assembly apparatus according to the present disclosure may be attached to or otherwise be incorporated in an end effector for a robot. Thus, as will be appreciated by one of skill in the art, an assembly apparatus according to the present disclosure may be used in any suitable application or combination of applications. Turning to the figures, specific non-limiting embodiments are described in further detail. It should be understood that the various systems, components, features, and methods described relative to these embodiments may be used either individually and/or in any desired combination as the disclosure is not limited to only the specific embodiments described herein. Fig.1 depicts an assembly apparatus 100 for placing a hung object 102 into a cavity 104 of a stationary object 106, according one illustrative embodiment. The first object is positioned vertically above the cavity of the second object relative to a direction of gravity G applied to the system and objects. Additionally, a portion of the first object oriented towards the cavity of the second object may be sized and shaped to be received in the cavity one assembled therewith. The assembly apparatus 100 includes a support structure 110 to which two or more flexible tethers 108 are attached. The two flexible tethers 108 are configured to be attached to and support the hung object 102 using any appropriate connection to portions of the hung object on opposing sides of a center of gravity of the hung object such that the hung object 102 is suspended from the support structure 110 via the flexible tethers 108. Further, the support structure 110 may be movable (e.g., up and down) via an actuator 112 (e.g., an overhead crane) such that the support structure and supported object may be selectively lowered towards the cavity. In the depicted embodiment, the actuator is part of a gantry crane such that the support structure may be moved in one or more horizontal directions relative to the depicted direction of gravity G to appropriately position the object relative to the cavity formed in the second object. Of course, the inclusion of an assembly apparatus as part of another either movable (e.g. a crane or other system) or stationary structure is also contemplated. In the illustrated embodiment, the assembly apparatus 100 is configured as a passive assembly system. In other words, tension in the flexible tethers 108 is maintained solely by a gravitational force G and the length of the flexible tethers 108 is fixed. Accordingly, as the actuator 112 moves the support structure 110 up and/or down, the hung object 102 moves up and/or down relative to the underlying second object 106 and cavity 104 formed therein respectively. Particularly, when the hung object 102 is suspended from the flexible tethers 108 and the flexible tethers 108 are held taut (e.g., under the gravitational force G), as the support structure 110 is moved a distance up and/or down, hung object 102 is moved an equal distance up and/or down. In this manner, the assembly apparatus 100 may lower the hung object 102 towards the cavity 104 of the stationary object 106 while a length and tension of the tethers 108 is maintained under the influence of gravity G. In turn, the stationary object 106 includes features that may help guide the corresponding portion of the hung object 102 into the cavity 104 during insertion. Particularly, a chamfer 114 may be formed in the second object such that the chamfer corresponding to an angled surface extending between an upper surface of the object and an inner surface of the cavity may extend at least partially, and in some instances completely, around an upper opening of the cavity 104 that is oriented towards and is configured to accept a corresponding portion of the hung object 102 into the cavity 104. The interaction between the chamfer 114 and a portion of the hung object 102 contacting the chamfer may aid in guiding the portion of the hung object into the cavity. For example, Fig. 2A illustrates hung object 102 in a position where a lower portion of the hung object 102 first makes contact with a portion of the chamfer 114 underlying the portion of the object to be inserted into the cavity. When the hung object 102 makes contact with the chamfer 114, the force distribution between the flexible tethers 108 may change causing an angle of the associated tethers to change as an orientation of the hung object changes as the hung object tilts to one side. Simultaneously, by appropriately controlling the length, angular orientation of the tethers, and/or applied forces for a given object, the portion of the hung object 102 contacting the chamfer may slide along the chamfer surface towards the cavity 104. In some instances, each of the tethers may remain tensioned with a non-zero tensile force applied to each tether during this initial contact and sliding in which case the hung object 102 may function as if it were connected to the support structure 110 by a rigid linkage. For instance, in the system shown in Fig.1A, the hung object may move and rotate as if it were attached to the support structure by a rigid four bar linkage where the object itself functions as one of the linkages. However, embodiments in which one or more tethers may go slack, i.e. have approximately zero tension applied, are also contemplated. In either case, the hung object 102 may be guided towards the cavity 104 by the chamfer 114 and the flexible tethers 108 such that an overall direction of movement of the portion of the hung object 102 contacting the chamfer is oriented at least partially inwards towards the cavity 104 of the stationary object 106 which may correspond to the contacting portion of the hung object sliding inwards towards the cavity along the chamfer surface. As noted above, and illustrated in Figs.2A-2C, the hung object 102 may be placed in a final position within the cavity 104 by sliding along a surface of the chamfer 114 into the cavity 104. Particularly, as shown in Fig.2A, when the hung object 102 contacts the chamfer 114, the hung object 102 slides along chamfer 114 until at least a portion of the hung object 102 enters the cavity 104. As shown in Fig.2B, the hung object 102 may initially make contact with an inner wall of the cavity 104 at a single point. As the hung object 102 continues to be lowered into the cavity 104 (e.g., by lowering the support structure 110), the hung object 102 may then make contact with the inner wall of the cavity 104 at two points, as shown in Fig.2C. Once the hung object 102 makes contact with the cavity 104 at two points, the reaction forces provided by the inner wall of the cavity 104 may serve to provide two points that constrain the orientation and insertion of the portion of the hung object to be inserted into the cavity. The cavity and corresponding portion of the hung object may be sized and shaped to permit the object to slide into the cavity without binding after this two-point contact engagement has occurred as the hung object continues to be lowered containment for insertion. This may permit the hung object 102 to be positioned in a final desired position within the cavity 104. Once the hung object 102 achieves a two-point contact state (e.g., as described herein), one of the flexible tethers 108 may go slack, while the other flexible tether 108 remains in tension. Thus, the combination of the reaction force from the inner wall of the cavity 104 in combination with the tension in the remaining taut tether may serve to control the hung object 102 to be lowered into the cavity 104 until the hung object 102 achieves a desired position within the cavity 104. In the delectated embodiment, tension is maintained in the remaining taut tether due to the gravitational force G acting on the tether. Alternatively or additionally, in some embodiments, the flexible tethers 108 may be actively controlled (e.g., as described herein in greater detail). In such embodiments, one or more actuators may actively control the tension in the flexible tethers 108 when the two-point contact state is achieved such that the hung object 102 may move towards a desired orientation. In such embodiments, the tension in the flexible tethers 108 may be controlled together or individually, depending on the application. In some embodiments, an assembly apparatus 100 may include features that allow the assembly apparatus 100 to maintain the hung object 102 in an approximately upright position when inserting the hung object 102 into the cavity 104. Particularly, the flexible tethers 108 may serve to minimize the angle between a longitudinal axis of the hung object 102 relative to a vertical axis A during insertion. For example, as shown in Fig.2A, the hung object may be approximately in line with the vertical axis A (e.g., as the flexible tethers 108 are held taut under the gravitational force G). However, as the hung object 102 slides along the chamfer 114, the hung object 102 may be angularly displaced relative to the central axis A, for example by a first angle α1, as shown in Fig.2B. Additionally, the hung object 102 may be angularly displaced relative to the central axis A by a second angle α2 during final insertion into the cavity. The flexible tethers 108 may be configured to orient the hung object 102 such that the angular displacement of the hung object 102 remains less than a threshold angle to facilitate both sliding of the object along the chamfer surface as well as insertion into the cavity without binding as described above. To help avoid binding during insertion of a portion of an object into a cavity, the flexible tethers may further serve to maintain the hung object 102 in an orientation such that the hung object 102 may fit within the cavity 104 as the hung object 102 is lowered into the cavity 104. Particularly, the flexible tethers 108 may hold the hung object 102 in an orientation such that as the hung object 102 slides along the chamfer 114 and/or enters an opening of the cavity 104 oriented towards the hung object, a horizontal transverse dimension of the hung object 102 is less than or equal to a horizontal transverse dimension of the opening of the cavity 104. Particularly, in the chamfer contact position shown in Fig.2A, a horizontal transverse dimension H1-A of the hung object 102 is less than or equal to a horizontal transverse dimension H2 of the cavity 104. Relatedly, in the one-point contact position shown in Fig.2B, a horizontal transverse dimension H1-B of the hung object 102 is less than or equal to the horizontal transverse dimension H2 of the cavity 104 such that the desired portion of the hung object may be inserted into the opening of the cavity. Further, in the two-point contact position shown in Fig.2C, a horizontal transverse dimension H1-C of the hung object 102 is less than or equal to the horizontal transverse dimension H2 of the cavity 104. While the above considerations have been described relative to a passive system with tethers that are not actively actuated, these concepts for facilitating sliding of a portion of an object contacting a chamfer and final insertion into a cavity are applicable to all of the embodiments described herein. Accordingly, actively controlled assembly apparatuses may be appropriately controlled to provide the above-noted functionality as well, as the disclosure is not limited in this fashion. As will be appreciated form the above, a hung object 102 may rotate (e.g., angularly displace) as the hung object 102 makes contact with and slides across a surface of a chamfer 114 to reach a final position in the cavity 104. Such rotation may occur about an instantaneous center of rotation P1 which may be related to the corresponding angle of the flexible tethers 108 relative to the hung object 102, see P1 and P2 in Figs.3A-3B. The instantaneous center of rotation may correspond to an imaginary point where lines that are parallel and coaxial with the tethers intersect with one another. Depending on the orientations of the tethers, the instantaneous center of rotation may either be above, below, or coincident with a bottom surface of the hung object. Particularly, in the configuration depicted in Fig.3A, the lines coaxial to the flexible tethers 108 intersect at point P1 which may be positioned vertically below a bottom surface of the hung object oriented towards a cavity of another object. Accordingly, the hung object 102 will tend to rotate about the point P1. Relatedly, in the configuration shown in Fig. 3B, the lines coaxial to the flexible tethers 108 intersect at point P2. Accordingly, the hung object 102 will tend to rotate about the point P2. As noted previously, in some instances, it may be desirable for the tethers to be oriented within particular angular ranges such that the center of instantaneous rotation of an object may be offset by some predetermined distance from the bottom surface of the object to facilitate sliding contact of the object with a corresponding chamfer and insertion into a cavity of a second object. For example, the points P1 and P2 may be selected such that the respective hung object in each figure may be appropriately oriented to fit within a corresponding cavity. Particularly, the hung object 102 may be oriented to fit within the cavity when the points P1, P2 are located outside of a lower region a-b of the object. Thus, the pivot points P1, P2 may be positioned vertically above or below the lower region a-b of the object as shown in the figures. Without wishing to be bound be theory, a location of the instantaneous center of rotation P1, P2 of a hung object relative to depicted region a-b may be a function of the angle between the flexible tethers 108 and a portion of the hung object the tethers are connected to as well as a length of the hung object 102 relative to the vertical direction parallel to the local direction of gravity G. For example, in the configuration shown in Fig.3A, the hung object 102 has a relatively small length L1, and the region a-b extends along most of the length L1. Accordingly, an angle ^1 between the flexible tethers 108 and a horizontal plane perpendicular to the direction of gravity may be set to be relatively large (e.g., nearly 90 degrees or another appropriate angle as elaborated on above), such that the pivot point P1 falls outside of region a- b. Relatedly, in the configuration shown in Fig.3B, the hung object 102 has a relatively long length L2 in the vertical direction, and the region a-b extends along only a small portion of the length L2. Accordingly, an angle ^2 between the flexible tethers 108 and the horizontal plane may be set to a variety of suitable values such that the pivot point P2 falls outside of the region a-b. Particularly, in the embodiment shown in Fig.3B, the angle ^2 is set to be relatively small such that the pivot point P2 is vertically above the region a-b. While the above embodiments show static tether lengths, it should be understood that tethers that have lengths and/or angles that are dynamically changed during operation using one or more actuators are also contemplated. Accordingly, the above discussion related to the instantaneous center of rotation and corresponding relationships may be applied to both passive and actively actuated assembly apparatuses as the disclosure is not so limited. Alternatively or in addition to the above, in some embodiments, an assembly apparatus 100 includes features that allow for active control of one or more parameters of the flexible tethers 108. For example, as shown in Fig.4, the assembly apparatus may include one or more actuators 118, depicted as an actuated arm, configured to actively control the flexible tethers 108. Particularly, the actuator 118 may be capable of controlling the extension and retraction of the flexible tethers 108 relative to a support structure 110 that the actuators and tethers are coupled to. Thus, the actuators may be used to lower or raise the hung object 102 relative to the support structure. As noted above, in some instances, it may be desirable to maintain a predetermined tension applied to the plurality of tethers used to support an object as it is lowered into a corresponding cavity. Accordingly, in some embodiments, an assembly apparatus 100 may include a plurality of sensors 116 that are configured to sense a tension and/or extension of the tethers 108. In the depicted embodiment, the sensors are depicted as for sensors that are positioned in line with, or attached to, the tethers. Regardless of the specific construction, the plurality of sensors may be operatively coupled to a processor 120 configured to control the one or more actuators 118 such that the sensors may output one or more sensed parameters to the processor. The processor may be operatively coupled with associated non-transitory processor readable memory that includes processor executable instructions that when executed by the processor may perform any of the methods disclosed herein. The processor 120 may control the one or more actuators 118 based at least in part on the one or more parameters sensed by the sensors. The processor 120 may then command the actuators to execute one or more functions on the flexible tethers 108. For example, the actuators may be controlled to maintain a tension in each tether greater than or equal to a predetermined tension while the hung object 102 is lowered relative to the support structure 110. For example, the tethers may be extended relative to the support structure while maintaining a tension in each of the tethers or the tethers may be operated to maintain the desired tension in each of the tethers while the support structure is lowered. In either case, the hung object may be lowered towards a cavity while maintaining a tension in each of the tethers during insertion of the object into the cavity. However, embodiments in which one or more of the tethers are permitted to go slack during an insertion process are also contemplated as the disclosure is not so limited. Fig.5 depicts one embodiment of a method that may be implemented to place a first object into a cavity of a second object using an assembly apparatus that includes passive operation where the tether lengths may be fixed as an object is lowered towards a cavity of an object including a chamfer extending at least partially around the cavity. In Fig.5, at step 500, a first object is suspended from the flexible tethers of an assembly apparatus in a desired orientation and horizontal position relative to a cavity of an object underlying the hung object such that a portion of the hung object be inserted into the cavity is roughly positioned and oriented towards the cavity. Once, the object is suspended in the desired orientation and position, at step 502, the object is lowered until the object contacts the chamfer of the cavity. Then, at step 504, the flexible tethers (e.g., tension) facilitates rotation of the object and sliding of a portion of the hung first object in contact with the chamfer towards the cavity, until the object is seated in the cavity. Finally, at step 506, the first object has slid across a surface of the chamfer such that the object makes a first contact, and subsequently a second contact, with one or more interior surfaces of the cavity prior to sliding to a desired final position within the cavity. In this passive arrangement, the operation of the system may simply include lowering of a support structure from which the tethers extend, and the overall configuration of the tethers and object may help to ensure the object slides appropriately across the various surfaces during insertion without binding, sticking, or moving in an undesired direction. Fig.6 is a flowchart illustrating an exemplary method of actively controlling the tensions applied to the tethers of a first hung object as the first object is inserted into a cavity of a second object disposed vertically below the first object relative to a direction of gravity. Similar to the above embodiment, at step 600 an assembly apparatus may be used to position and orient the first object while it is suspended from the flexible tethers towards a corresponding cavity formed in a second object underlying the first object. This may either be done manually and/or a support structure of the apparatus may be moved to a desired position and orientation using one or more corresponding actuators as the disclosure is not limited in how the first object is positioned and oriented relative to the second object. In either case, one or more actuators of the assembly apparatus may be appropriately controlled to extend (i.e. lengthen the flexible tethers) to lower the first object towards the second object at step 602. As the first object is lowered, a tension in each of the tethers may be sensed at 604 such that a forced based control loop may be implemented to control the actuators associated with the tethers. For example, in some embodiments, the actuators may be operated to extend the associated tethers so long as the sensed tension in the tether is greater than or equal to a predetermined threshold. Correspondingly, extension of a particular tether may be stopped, and in some instances a tether may be retracted when a sensed tension is less than the predetermined threshold. In this manner, tension may be maintained in each of the flexible tethers as the object is lowered into a cavity at 606. Again, this may help to facilitate the sliding of a portion of the first hung object contacting a chamfer surrounding the cavity towards the cavity as well as the subsequent insertion of the portion of the first hung object into the cavity. Example 1: Conditions for Successful No Slack/No Stick Insertion Referring to Fig.15A and without wishing to be bound by theory, the hung object 102 is held only by the two tethers 108 in the depicted embodiment. Accordingly, in the depicted embodiment, neither of the two flexible tethers 108 go slack (e.g., by angling the tethers such that each tether does not fall within the region a-b, as shown in Figs.3A-3B). Without wishing to be bound by theory, under such “No-Slack” conditions, the quasi- static motion of the hung object 102 may be kinematically determined. Since both flexible tethers 108 are taut, the flexible tethers 108 may be treated as a pair of rigid links. The support structure 100, the two taut flexible tethers 108, and the hung object 102 form a four-bar-linkage within a vertical plane with just one degree of freedom. Figs.7 and 15A show insertion of such a hung object 102 under the “No-Slack” conditions described above. As the hung object 102 lands on a surface of a chamfer 114, the hung object 102 is constrained by the contact with the chamfer 114. Without wishing to be bound by theory, the position and orientation of the hung object may be determined geometrically. As the support structure 110 is lowered, position and orientation of the hung object 102 may vary in relation to a height of the support structure 110. After reaching a bottom edge of the cavity 104, the hung object 102 may contact the edge of the cavity 114 at its side, making one point contact with a portion of the cavity 104. Without wishing to be bound by theory, in the one-point contact state, the position and orientation of the hung object 102 may be kinematically determined. This continues until the hung object 102 contacts an inner wall of the cavity 104 two points, achieving a two-point contact state. In the two-point contact state, the hung object 102 may be constrained on at least two sides of the cavity 104. Once the hung object 102 is so constrained, the four-bar-linkage is no longer formed. Without wishing to be bound by theory, in such a condition. at least one flexible tether 108 may go slack to meet the two-point contact constraint conditions. In such a scenario, a unidirectional nature of tension in the flexible tethers (e.g., the ability for the flexible tethers 108 to be tensioned by gravity) releases the tension in one or more of the flexible tethers 108, so that the hung object 102 may not be over-constrained. In the embodiment shown in Figs.7 and 15A, the “No-Slack” conditions described above may be maintained throughout the insertion process until two-point contact occurs so that the movement of the hung object 102 may be kinematically controlled, as detailed above. By employing appropriate tether angles ϕ₁, ϕ₂ and locations of tether attachment such that an instantaneous center of rotation P3 may be located away from the region a-b, the hung object 102 may be guided through the quasi-static process to reach the two-point contact state at a depth within the cavity 104 sufficient for the insertion to succeed. Such “No-Slack” conditions may be met in two ranges of tether orientations: small angles and large angles. In some instances, employing mid-range angles may result in the instantaneous center of rotation P3 falling within region a-b, violating the “No-Slack” condition. Without wishing to be bound by theory, the choice of tether angles may depend on the dimensions of a hung object 102. Fig.3A-3B illustrate two such examples. If the hung object 102 has a relatively short overall length L1, a large tether angle ^1 may be employed, for example to position an instantaneous center of rotation of the hung object 102 below region a-b. On the other hand, if the hung object 102 has a relatively long overall length L2, a smaller tether angle ^2 may be employed, for example to position an instantaneous center of rotation of the hung object 102 above region a-b. Turning to the insertion process, it may be desirable to prevent the hung object 102 from sticking to a surface of the chamfer 114. To control for this fact, the inventors first considered the conditions necessary for the hung object 102 to stick to a surface of the chamfer 114. This may occur either at a moment that a portion of the hung object 102 contacts a surface of the chamfer 114 or while the hung object 102 slides along the chamfer 114. When the hung object 102 sticks to the surface of the chamfer 114, the hung object 102 may lose two degrees of freedom. Without wishing to be bound by theory, in such a scenario, the hung object 102 may only rotate about the point of contact, implying that at least one tether goes slack. Alternatively, if the flexible tethers 108 are set with an appropriate angle such that the instantaneous center of rotation P3 does not fall within region a-b, the hung object 102 may not stick to a surface of chamfer 114 during insertion. Using the parameters defined in Fig. 7, the No-Slack conditions on the cable angles are given by the following equations:

Without wishing to be bound by theory, the equation above may be used to determine two sets of tether angle ranges that may be associated with two scenarios: sticking on a surface of the chamfer 114 during insertion and when and sliding along a surface of the chamfer 114 during insertion. Without wishing to be bound by theory, the static coefficient of friction may be used to determine sticking upon first contact with the chamfer 114 and the kinetic coefficient of friction may be used while sliding down the chamfer 114. Similar equations may be derived to determine the sticking conditions during one point contact. It should be noted, however, that “No-Sticking” conditions described above alone do not guarantee that the hung object 102 slides down the chamfer 114. The hung object 102 may stay on the chamfer surface under certain kinematic conditions. For example, case (B) shown in Fig. 15B shows a case where the hung object 102 may not slide, but instead stays on the chamfer 114. In the configuration of case (B) of Fig.15B, the instantaneous center of rotation P3-B is located at an end of the hung object 102, where the extensions of the two tethers 108 intersect. Without wishing to be bound by theory, suppose that the left corner of the hung object 102, point A in Fig.7, touches the chamfer. As the hung object 102 rotates about P3-B, point A is moved upwards. If this upward movement equals a downward movement of the support structure 110, the two displacements cancel, and the hung object 102 may not slide, but instead stay stationary on the chamfer 114. This stationary behavior may be a function of the tether angles, the relative location of point A to the instantaneous center of rotation, and/or the chamfer angle α, as shown in Fig.15A. Additional scenarios were determined relative to the location of the instantaneous center of rotation located slightly above the bottom surface of the object P3-C in Fig.15C, located at a larger distance above the bottom surface of the object P3-D in Fig.15D, and at a location below the bottom surface of the object P3-E in Fig.15E. As can be seen in these figures, locations of an instantaneous center of rotation that are at larger distances above and below a bottom surface of the portion of the object to be inserted into the cavity may result in rotations of the portion contacting the chamfer that are directed towards an interior of the chamfer where the cavity is located. Accordingly, the tethers of an assembly apparatus may be appropriately configured and/or controlled such that the instantaneous center of rotation of an object may be positioned appropriately to provide sliding motion of the portion of the object contacting the chamfer surface towards an opening of the cavity. Without wishing to be bound by theory, if both the “No-Sticking” and “No-Stationary” conditions described above are satisfied, the hung object 102 may be expected to slide along the chamfer 114. After the hung object 102 crosses chamfer 114, an opposite side of the bottom surface of the hung object 102 (e.g., point B in Fig.7), may clear the width of the cavity 104 (e.g., H2 in Figs.2A-2C). Without wishing to be bound be theory, a four-bar linkage analysis may be employed to estimate a tilt angle of the hung object 102 at a point in which the hung object 102 has reached the end of the chamfer 114 and just before transitioning to the one-point contact state described herein. Without wishing to be bound by theory, as the equation below describes, if the predicted tilt angle of the hung object 102 meets the specified constraint, the opposite side of the bottom surface of the hung object 102 may be able to clear a corresponding edge of the cavity 104, as shown in Fig. 7.

Subsequently, the hung object 102 may reach a two-point contact state when at least the opposite side of the bottom surface of the hung object 102 touches a corresponding edge of the cavity 104. Without wishing to be bound by theory, a depth of the first two-point contact position may determine whether the hung object 102 sticks inside of the cavity 104, for example becoming wedged within the cavity 104. Wedging may be less likely to occur when the depth of the first two-point contact position is sufficiently deep within the cavity 104. Depending on the given geometry of a hung object 102, certain tether angles may yield a deeper depth of the first two-point contact position than others, making wedging less likely. Such parameters may be chosen to such that the depth of the first two-point contact position is as deep as possible. Without wishing to be bound by theory, the depth of the first two-point contact position may be determined kinematically and geometrically. Example 2: Experimental Verification Analytical results associated with embodiments of the apparatus and method disclosed herein were validated through experiments using both 2D and 3D scale models. For example, as shown in Fig. 8, a steel peg 126 (.76 kg) was manufactured to slide into a steel hole 132 with a chamfer angle of 45 degrees. To avoid nonlinearities associated with sharp edges, the bottom corners of the peg 126 were given a fillet of 0.6mm. The peg 126 was connected to the mounting system via low-stretch polyester rope 134 and the mounting system was attached to a linear guide rail 122 that was powered by a lead screw. April Tags were affixed to the mounting system, the peg 126 and to the hole 132 to provide relative location data for calculations as well as provide an angle of tilt of the peg. Indicator LEDs 128 provide a trigger as to when the two- point contact state was achieved (e.g., as described in greater detail herein). Various types of materials were placed on the chamfer surface to vary the coefficient of friction of the interaction between the peg and the chamfer (e.g., material 130). The coefficient of friction was measured by placing a piece of the material 130 on a steel block and resting the peg 126 on top of the surface. The angle of the steel block was raised until the peg 126 began to slide along the surface. The angle at which sliding began to occur was measured to be the coefficient of friction angle, fs where m = tan(fs). In this experiment, the length L of the peg 126 was set to 127mm, and the width d of the peg 126 was set to 50.8 mm. Moreover, a chamfer angle α was set to 45 degrees, and the lengths l1, l2 of the flexible tethers 134 was set to 203.2 mm. A diameter Dh of the hole was set to 51.82 mm, meaning the clearance between the peg 126 and the hole was 1.02mm. First, an experiment was conducted to verify a successful chamfer crossing of the peg 126 when the flexible tether angles are in both the allowable (e.g., such that the pivot point is outside of region a-b as described above in relation to Figs.3A-3B) and not-allowable regions (e.g., such that the pivot point is located within region a-b as described above in relation to Figs. 3A-3B) using three different coefficients of friction. As seen in Fig.9, as the coefficient of friction of the peg-hole system increases, the range for allowable initial angles decreases drastically. This experiment verified that the peg 126 would sliding in the allowable region. Second, an experiment was conducted in which the simulation of quasi-static chamfer crossing was compared with the actual peg crossing the chamfer for different initial peg horizontal errors. Turning back to Fig.7, e₀ values of 1.27mm, 2.54mm, and 5.08mm, which represent 2.5%, 5% and 10% of the diameter of the experimental peg respectively, were tested. As shown in Fig.10, the data points indicate experimentally measured data, and the lines indicate the predicted values from the simulation. A root mean squared error (RMSE) was calculated between the measured and predicted results. For horizontal error e₀ = 1:27mm, the RMSE was 0.5 degrees, for e₀ = 2:54mm the RMSE was 1 degree and for e₀ = 5:08mm the RMSE was 2.4 degrees. This indicates that the kinematic analysis can be used to predict the final angle of the peg at the end of the chamfer crossing for approximately all ranges of flexible tether angles to within 2.4 degrees. Third, an experiment was conducted in which the depth at first two-point contact (e.g., as described herein as part of the trajectory associated with insertion) was measured based on different horizontal displacement errors of the peg and different flexible tether mounting angles. A root mean squared error was calculated between the measured and predicted results. For horizontal error of e₀ = 1:27mm, the RMSE was 8.9 mm, for e₀ = 2:54mm the RMSE was 4.2 mm and for e₀ = 5:08mm the RMSE was 8.6 mm. This indicates that the kinematic model may be trusted to predict the depth of first two-point contact to within 7.5% of the peg length for the largest amount of horizontal displacement error the peg may be expected to experience. As seen in Fig.10, the depth associated with achieving two-point contact l* decreases as the flexible tether angles increase. Additionally, as shown in Fig.10, the depth l* increases as the flexible tether angles approach 90 degrees. This implies that to configure the assembly apparatus to insert the peg such that an appropriate two-point contact depth l* is achieved, the flexible tether angles may be either as small as possible (e.g., as shown in Fig.3B) or as close to 90 degrees as possible (e.g., as shown in Fig.3A). Fourth, additional trials were conducted using a 3D setup, as shown in Fig.11, consisting of a 3.5kg aluminum round peg that is 101.7mm in diameter and 152.4mm long, an aluminum hole with an inner diameter of 101.85mm, low-stretch polyester ropes that are 457mm and 609.6 mm long, and a mounting plate that is 203.2mm in diameter. The results of the trials, depicted in Fig.11, show that for certain cable angles, the peg does not successfully cross the chamfer and enter the hole. The lines depicting the travel trajectories in which the cable mounting angle is inside the predicted not-allowable region (e.g., region a-b as shown in Figs.3A-3B) for the specific peg geometry. In these cases, the peg may tip forward and topple over. Accordingly, Fig.11 shows a minimal change in the distance of the center of the peg to the center of the hole and the depth of the peg within the hole, within such a region. Particularly, the peg insertion was found to be successful when the flexible tethers are outside this range, specifically when they are mounted at 76 degrees and/or 38 degrees from horizontal. Example 3: Parameter Study Without wishing to be bound by theory, in some instances, the mechanical behavior of a suspended object, such as a peg, may be determined by applying kinematic principles associated with a four-bar linkage. Particularly, the effect of varying the length L of the hung object 102, the width d of the hung object 102, and the chamfer angle α was studied. The trajectories of hung objects 102 with varying geometric parameters and varying the initial cable placement angles were determined, and the instantaneous slope at the point of first contact with the chamfer 114 was calculated. If the slope of the instantaneous trajectory was conducive to the hung object 102 sliding down the chamfer, the configuration was deemed allowable. The results of the parameter study are depicted in Figs.12-14. The inventors observed that as the length L of the hung object 102 increased, the region in which the peg will appear stationary increases and the region in which a sticking phenomenon may occur shifts towards a region of higher cable angles. Accordingly, the inventors understood that small cable angles may be associated with success of insertion (e.g., as shown in Fig.3B). Additionally, the inventors observed that as the width d of the hung object 102 increases, the region in which the sticking phenomenon may occur increases, while the region in which the hung object 102 may be stationary appears to stay approximately the same. Also, the inventors observed that as the chamfer angle α becomes less steep, a range of valid mounting configurations decreases. The above-described embodiments of the technology described herein can be implemented in any of numerous ways. For example, the embodiments may be implemented using hardware, software, or a combination thereof. When implemented in software, the software code can be executed on any suitable processor or collection of processors, whether provided in a single computing device or distributed among multiple computing devices. Such processors may be implemented as integrated circuits, with one or more processors in an integrated circuit component, including commercially available integrated circuit components known in the art by names such as CPU chips, GPU chips, microprocessor, microcontroller, or co-processor. Alternatively, a processor may be implemented in custom circuitry, such as an ASIC, or semicustom circuitry resulting from configuring a programmable logic device. As yet a further alternative, a processor may be a portion of a larger circuit or semiconductor device, whether commercially available, semi-custom or custom. As a specific example, some commercially available microprocessors have multiple cores such that one or a subset of those cores may constitute a processor. Though, a processor may be implemented using circuitry in any suitable format. Also, the processor may have one or more input and output devices. These devices can be used, among other things, to present a user interface. Examples of output devices that can be used to provide a user interface include display screens for visual presentation of output and speakers or other sound generating devices for audible presentation of output. Examples of input devices that can be used for a user interface include keyboards, individual buttons, and pointing devices, such as mice, touch pads, and digitizing tablets. As another example, a computing device may receive input information through speech recognition or in other audible format. Such processors may be interconnected by one or more networks in any suitable form, including as a local area network or a wide area network, such as an enterprise network or the Internet. Such networks may be based on any suitable technology and may operate according to any suitable protocol and may include wireless networks, wired networks or fiber optic networks. Also, the various methods or processes outlined herein may be coded as software that is executable on one or more processors that employ any one of a variety of operating systems or platforms. Additionally, such software may be written using any of a number of suitable programming languages and/or programming or scripting tools, and also may be compiled as executable machine language code or intermediate code that is executed on a structurework or virtual machine. In this respect, the embodiments described herein may be embodied as a computer readable storage medium (or multiple computer readable media) (e.g., a computer memory, one or more floppy discs, compact discs (CD), optical discs, digital video disks (DVD), magnetic tapes, flash memories, RAM, ROM, EEPROM, circuit configurations in Field Programmable Gate Arrays or other semiconductor devices, or other tangible computer storage medium) encoded with one or more programs that, when executed on one or more computers or other processors, perform methods that implement the various embodiments discussed above. As is apparent from the foregoing examples, a computer readable storage medium may retain information for a sufficient time to provide computer-executable instructions in a non-transitory form. Such a computer readable storage medium or media can be transportable, such that the program or programs stored thereon can be loaded onto one or more different computing devices or other processors to implement various aspects of the present disclosure as discussed above. As used herein, the term "computer-readable storage medium" encompasses only a non- transitory computer-readable medium that can be considered to be a manufacture (i.e., article of manufacture) or a machine. Alternatively or additionally, the disclosure may be embodied as a computer readable medium other than a computer-readable storage medium, such as a propagating signal. The terms “program” or “software” are used herein in a generic sense to refer to any type of computer code or set of computer-executable instructions that can be employed to program a computing device or other processor to implement various aspects of the present disclosure as discussed above. Additionally, it should be appreciated that according to one aspect of this embodiment, one or more computer programs that when executed perform methods of the present disclosure need not reside on a single computing device or processor but may be distributed in a modular fashion amongst a number of different computers or processors to implement various aspects of the present disclosure. Computer-executable instructions may be in many forms, such as program modules, executed by one or more computers or other devices. Generally, program modules include routines, programs, objects, components, data structures, etc. that perform particular tasks or implement particular abstract data types. Typically, the functionality of the program modules may be combined or distributed as desired in various embodiments. Various aspects of the present disclosure may be used alone, in combination, or in a variety of arrangements not specifically discussed in the embodiments described in the foregoing and is therefore not limited in its application to the details and arrangement of components set forth in the foregoing description or illustrated in the drawings. For example, aspects described in one embodiment may be combined in any manner with aspects described in other embodiments. The embodiments described herein may be embodied as a method, of which an example has been provided. The acts performed as part of the method may be ordered in any suitable way. Accordingly, embodiments may be constructed in which acts are performed in an order different than illustrated, which may include performing some acts simultaneously, even though shown as sequential acts in illustrative embodiments. Further, some actions are described as taken by a “user.” It should be appreciated that a “user” need not be a single individual, and that in some embodiments, actions attributable to a “user” may be performed by a team of individuals and/or an individual in combination with computer-assisted tools or other mechanisms. Use of ordinal terms such as “first,” “second,” “third,” etc., in the claims to modify a claim element does not by itself connote any priority, precedence, or order of one claim element over another or the temporal order in which acts of a method are performed, but are used merely as labels to distinguish one claim element having a certain name from another element having a same name (but for use of the ordinal term) to distinguish the claim elements. Also, the phraseology and terminology used herein is for the purpose of description and should not be regarded as limiting. The use of “including,” “comprising,” or “having,” “containing,” “involving,” and variations thereof herein, is meant to encompass the items listed thereafter and equivalents thereof as well as additional items. While the present teachings have been described in conjunction with various embodiments and examples, it is not intended that the present teachings be limited to such embodiments or examples. On the contrary, the present teachings encompass various alternatives, modifications, and equivalents, as will be appreciated by those of skill in the art. Accordingly, the foregoing description and drawings are by way of example only.

Claims

CLAIMS What is claimed is: 1. An assembly apparatus comprising: a support structure; a plurality of tethers suspended from the support structure, the plurality of tethers configured to suspend a first object from the support structure; and one or more actuators operatively coupled to at least one selected from the group of the support structure and the plurality of tethers, the one or more actuators configured to lower a portion of the first object under an influence of gravity towards a cavity formed in a second object with a chamfer formed along at least a portion of the cavity, and wherein the one or more actuators and the plurality of tethers are configured to control the lowering of the portion of the object such that the portion of the first object contacts and slides along the chamfer as the portion of the first object is inserted into the cavity.

2. The assembly apparatus of claim 1, wherein the one or more actuators are configured to maintain a predetermined tension in each tether of the plurality of tethers as the portion of the first object is lowered into the cavity.

3. The assembly apparatus of claim 1, wherein the one or more actuators are configured to lower the support structure.

4. The assembly apparatus of claim 3, wherein the one or more actuators include a plurality of actuators configured to extend the plurality of tethers to lower the first object.

5. The assembly apparatus of claim 4, wherein the plurality of tethers includes one or more sensors configured to sense a tension of the plurality of tethers.

6. The assembly apparatus of claim 5, wherein the one or more actuators are configured to modify the tension of the plurality of tethers based at least in part on the sensed tension.

7. The assembly apparatus of claim 6, wherein the one or more actuators are configured to be controlled by a processor based at least in part on the sensed tension.

8. The assembly apparatus of claim 1, wherein the one or more actuators and the plurality of tethers are configured to maintain the first object approximately upright while the first object is lowered into the cavity of the second object.

9. The assembly apparatus of claim 1, wherein the plurality of tethers includes two tethers configured to move the first object in two dimensions.

10. The assembly apparatus of claim 1, wherein the plurality of tethers includes three tethers configured to move the first object in three dimensions.

11. The assembly apparatus of claim 1, wherein the one or more actuators are configured to move the object such that a magnitude of movement of the portion of the first object towards the cavity of the second object is greater than a magnitude of movement of the portion of the first object away from the cavity of the second object as the first object slides along the chamfer of the second object.

12. The assembly apparatus of claim 1, wherein lines extending coaxially with the plurality of tethers intersect at an intersection point, and wherein the intersection point is offset by a predetermined distance in a vertical direction from a bottom surface of the portion of the first object oriented towards the cavity, wherein the vertical direction is parallel to a direction of gravity.

13. The assembly apparatus of claim 12, wherein the predetermined distance is offset from the bottom surface by at least 50% of an overall length of the first object, wherein the overall length is parallel to a direction of gravity.

14. The assembly apparatus of claim 12, wherein the assembly apparatus further includes a processor configured to control the one or more actuators such that lengths of each tether of the plurality of tethers are set such that the intersection point is offset from the bottom surface by at least the predetermined distance.

15. A method of placing an object in a cavity comprising: suspending a first object from a plurality of tethers of an assembly apparatus; lowering a portion of the first object under an influence of gravity towards a cavity formed in a second object with a chamfer formed along at least a portion of the cavity such that at least a portion of the first object makes contact with the chamfer; sliding the portion of the first object along the chamfer; and placing the first object in the cavity of the second object.

16. The method of claim 15, wherein lowering the first object into the cavity of the second object includes lowering the plurality of tethers.

17. The method of claim 16, wherein lowering the plurality of tethers includes maintaining a predetermined tension in each tether of the plurality of tethers as the portion of the first object is lowered into the cavity of the second object.

18. The method of claim 15, wherein lowering the first object into the cavity includes maintaining the first object approximately upright.

19. The method of claim 15, wherein sliding the portion of the first object along the chamfer includes moving the first object such that a magnitude of movement of the portion of the first object towards the cavity of the second object is greater than a magnitude of movement of the portion of the first object away from the cavity of the second object.

20. The method of claim 15, wherein suspending the first object from the plurality of tethers of the assembly apparatus includes suspending the first object such that lines extending coaxially with the plurality of tethers intersect at an intersection point, and wherein the intersection point is offset by a predetermined distance in a vertical direction from a bottom surface of the portion of the first object oriented towards the cavity, wherein the vertical direction is parallel to a direction of gravity.